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A group analysis approach for a nonlinear differential system arising in diffusion phenomena. (English) Zbl 0872.35004
The authors consider a class of systems of differential equations of the special form \[ u_t= h(u,v),\quad v_t= [g(v) v_x+ f(v)u_x]_x, \] which arises in diffusion phenomena (diffusion of a solvent into a polymer slab). Using equivalence transformations, they give a classification, then Lie symmetries and classes of exact solutions are computed in special cases.

MSC:
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35C05 Solutions to PDEs in closed form
35K57 Reaction-diffusion equations
35Q80 Applications of PDE in areas other than physics (MSC2000)
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